Coterminals and reference angles

Question

1. List three angles that are co-terminal with 78º.

2. Convert 255º to radians. Find the exact value, leave your answer in terms of pi and enter all work.

3. What is a reference angle? Make sure your create an example of using a reference angle as part of your explanation.

Answer 1

Hi Anessa S.

Coterminal angles include, angles formed by 78° + 360° and 78 + multiplies of 360°, and 78° - 360° and 78° - multiplies of 360°

438°

798°

-282°

642°

Reference angles are with respect to the quadrant

1. The reference angle is the positive acute angle that can represent an angle of any measure. The reference angle must be < 90 ∘. In radian measure, the reference angle must be < π/2. Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees.
2. For -282° the reference angle is still -282 + 360 = 78°

Check the internet for illustration of reference angles regardless of the rotation of the terminal end of the angle, since rotations can be Counter Clockwise or Clockwise

Conversion from degrees to radians is

Angle in degrees (π/180 degrees)

255 degrees(π/180 degrees)